3 Answers
3

Typically software developer parlance is "screens", "pages" is more about websites. Windows is also used.

In applications where there are sub-sections there are often separate screens that might be more accurately referred to as "menus" and "modules", depending on if they open a new screen or window. This is true of mobile app development, and even web apps - but not web sites, where pages is used.

For immersive enviroments there are rooms, areas and levels and other more specifically descriptive terms for new pages or screens.

I would go with the same i.e. page. This would be making it easier to know what you refer to since it's a convention on web sites. User Interface refers more to the entire application, which contains several pages - like a web site also have several pages. Furthermore you don't have to distinguish between web apps or native apps.